Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div113" type="section" level="1" n="19">
          <pb o="88" file="0106" n="106" rhead=""/>
          <p>
            <s xml:id="echoid-s5650" xml:space="preserve">Nam erit tum CA. </s>
            <s xml:id="echoid-s5651" xml:space="preserve">CR = CA. </s>
            <s xml:id="echoid-s5652" xml:space="preserve">CK + NK. </s>
            <s xml:id="echoid-s5653" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s5654" xml:space="preserve">unde, com-
              <lb/>
            munem utrinque adjiciendo rationem CK ad CA, erit CK. </s>
            <s xml:id="echoid-s5655" xml:space="preserve">CA
              <lb/>
            + CA. </s>
            <s xml:id="echoid-s5656" xml:space="preserve">CR = CA. </s>
            <s xml:id="echoid-s5657" xml:space="preserve">CK + CK. </s>
            <s xml:id="echoid-s5658" xml:space="preserve">CA + NK. </s>
            <s xml:id="echoid-s5659" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s5660" xml:space="preserve">hoc eſt
              <lb/>
            CK. </s>
            <s xml:id="echoid-s5661" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5662" xml:space="preserve">: NK. </s>
            <s xml:id="echoid-s5663" xml:space="preserve">NA.</s>
            <s xml:id="echoid-s5664" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5665" xml:space="preserve">Notetur in figuris ſequentibus eſſe perpetuo CA. </s>
            <s xml:id="echoid-s5666" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5667" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s5668" xml:space="preserve">R.
              <lb/>
            </s>
            <s xml:id="echoid-s5669" xml:space="preserve">
              <note position="left" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">Fig. 130,
                <lb/>
              131.</note>
            quod ſemel, brevitatis causâ, monitum efto.</s>
            <s xml:id="echoid-s5670" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5671" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s5672" xml:space="preserve">Hinc conſectatur; </s>
            <s xml:id="echoid-s5673" xml:space="preserve">primò; </s>
            <s xml:id="echoid-s5674" xml:space="preserve">Si fuerit AN &</s>
            <s xml:id="echoid-s5675" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5676" xml:space="preserve">CR, quòd re-
              <lb/>
            fractus N _a_ cum axe AC prorsùm excurrens conveniet. </s>
            <s xml:id="echoid-s5677" xml:space="preserve">Nam erit
              <lb/>
              <note position="left" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">Fig. 129.</note>
            CK. </s>
            <s xml:id="echoid-s5678" xml:space="preserve">AN &</s>
            <s xml:id="echoid-s5679" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5680" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s5681" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5682" xml:space="preserve">: NK. </s>
            <s xml:id="echoid-s5683" xml:space="preserve">AN. </s>
            <s xml:id="echoid-s5684" xml:space="preserve">adeóque CK &</s>
            <s xml:id="echoid-s5685" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5686" xml:space="preserve">NK.</s>
            <s xml:id="echoid-s5687" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5688" xml:space="preserve">V. </s>
            <s xml:id="echoid-s5689" xml:space="preserve">Secundò; </s>
            <s xml:id="echoid-s5690" xml:space="preserve">ſi fuerit AN = CR, refractus N _a_ ad AC pa-
              <lb/>
              <note position="left" xlink:label="note-0106-03" xlink:href="note-0106-03a" xml:space="preserve">Fig. 130.</note>
            rallelus erit.</s>
            <s xml:id="echoid-s5691" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5692" xml:space="preserve">Nam ſit NH ad AC parallela. </s>
            <s xml:id="echoid-s5693" xml:space="preserve">quum itaque ſit CA. </s>
            <s xml:id="echoid-s5694" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s5695" xml:space="preserve">:
              <lb/>
            (CA. </s>
            <s xml:id="echoid-s5696" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5697" xml:space="preserve">: ) I. </s>
            <s xml:id="echoid-s5698" xml:space="preserve">R; </s>
            <s xml:id="echoid-s5699" xml:space="preserve">erit AN ipſius HN refractus. </s>
            <s xml:id="echoid-s5700" xml:space="preserve">ergò viciſſim
              <lb/>
            N Hipſius AN.</s>
            <s xml:id="echoid-s5701" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5702" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s5703" xml:space="preserve">Tertiò; </s>
            <s xml:id="echoid-s5704" xml:space="preserve">Si fuerit AN &</s>
            <s xml:id="echoid-s5705" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5706" xml:space="preserve">CR, refractus N _a_ cum AC
              <lb/>
              <note position="left" xlink:label="note-0106-04" xlink:href="note-0106-04a" xml:space="preserve">Fig. 131.</note>
            retrò conveniet extractus.</s>
            <s xml:id="echoid-s5707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5708" xml:space="preserve">Erit enim tunc CK. </s>
            <s xml:id="echoid-s5709" xml:space="preserve">AN &</s>
            <s xml:id="echoid-s5710" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5711" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s5712" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5713" xml:space="preserve">: NK. </s>
            <s xml:id="echoid-s5714" xml:space="preserve">AN. </s>
            <s xml:id="echoid-s5715" xml:space="preserve">ac indè
              <lb/>
            CK &</s>
            <s xml:id="echoid-s5716" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5717" xml:space="preserve">NK.</s>
            <s xml:id="echoid-s5718" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5719" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s5720" xml:space="preserve">Hinc clarum eſt; </s>
            <s xml:id="echoid-s5721" xml:space="preserve">Si fuerit AB non minor quàm CR, om-
              <lb/>
            nes refractos verſus AC procurrentes convergere. </s>
            <s xml:id="echoid-s5722" xml:space="preserve">erit enim tunc
              <lb/>
            ſemper AN &</s>
            <s xml:id="echoid-s5723" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5724" xml:space="preserve">CR.</s>
            <s xml:id="echoid-s5725" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5726" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s5727" xml:space="preserve">Subnotetur autem ſi fuerit ſaltem AB = CR; </s>
            <s xml:id="echoid-s5728" xml:space="preserve">axi propio-
              <lb/>
            res radios in ſenſibilem paralleliſmum refringi.</s>
            <s xml:id="echoid-s5729" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5730" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s5731" xml:space="preserve">Item, Si AT circulum tangat, & </s>
            <s xml:id="echoid-s5732" xml:space="preserve">fuerit AT &</s>
            <s xml:id="echoid-s5733" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5734" xml:space="preserve">CR; </s>
            <s xml:id="echoid-s5735" xml:space="preserve">ma-
              <lb/>
            nifeſtum eſt omnes refractos retrò protractos cum AC concurrere.
              <lb/>
            </s>
            <s xml:id="echoid-s5736" xml:space="preserve">tunc enim ſemper eſt AN &</s>
            <s xml:id="echoid-s5737" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5738" xml:space="preserve">CR.</s>
            <s xml:id="echoid-s5739" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5740" xml:space="preserve">X. </s>
            <s xml:id="echoid-s5741" xml:space="preserve">Clarum eſt quoque, ſi AN = CR, omnes arcui BN inci-
              <lb/>
            dentium refractos retrò productos, omnes autem arcui NT inciden-
              <lb/>
            tium refractos antrorſum procurrentes axi occurrere.</s>
            <s xml:id="echoid-s5742" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5743" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s5744" xml:space="preserve">Quum autem in caſu, propoſiti maximè contrario (quum
              <lb/>
            nempe I &</s>
            <s xml:id="echoid-s5745" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5746" xml:space="preserve">R; </s>
            <s xml:id="echoid-s5747" xml:space="preserve">& </s>
            <s xml:id="echoid-s5748" xml:space="preserve">radii concavis incidunt partibus) adſimilis contingat
              <lb/>
            diverſitas, hanc quoqne breviter attingemus.</s>
            <s xml:id="echoid-s5749" xml:space="preserve"/>
          </p>
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